# Reynolds number and the relationship with lift and drag.

1. Oct 22, 2012

### Brettcm

Hello

I am preparing for my aerodynamics exam and I'm having trouble with this question.

Why is the Reynolds number of the airflow over a wing important in determining the value of lift and drag

The Reynolds number is important for determining laminar and turbulent flows over a body. It is a dimensionless number and expresses
the ratio of inertial forces to viscous forces. A Reynolds number less than 5 x 105 is likely to be laminar whereas a Reynolds number greater
than 5 x 105 will most likely be turbulent.

The Reynolds number is important for determining drag as we can use it to calculate the length of the laminar and turbulent flow
over a wing. Moreover we can use this to calculate the friction coefficient (skin friction drag) acting on the wing.

Laminar Flow

Cf = $\frac{1.328}{\sqrt[]{}Re}$

Turbulent Flow

Cf = $\frac{0.074}{\sqrt[]{}Re^{2}}$

It is important for calculating lift because as Reynolds number increases, the maximum lift coefficient increases. But this does not occur
indefinitely; when flows become very turbulent, the maximum lift coefficient begins to drop and so does the overall lift coefficient.

Re = $\frac{ρV×}{\mu}$

ρ = Density
V = Velocity of the free-stream airflow
× = The characterised length of the aerofoil
$\mu$ = The fluid viscosity

I would like to know if the way I have explained the Reynolds number is correct particularly with reference to lift, and is the Reynolds number important when
dealing with other types of drag?

Thanks!

2. Oct 22, 2012